NEW YORK (Reuters) - Families of Sept. 11 victims and others who may seek to sue foreign governments accused of supporting terrorism in the United States still face significant legal hurdles, despite a boost from passage of a law allowing such cases to proceed.

The new Justice Against Sponsors of Terrorism Act, or JASTA, grants an exception to the legal principle of sovereign immunity in cases of terrorism on U.S. soil.

Passage of the law over a presidential veto could allow relatives and survivors of the Sept. 11, 2001 attacks to move forward with a case they filed more than a decade ago against Saudi Arabia in New York federal court.

Still, it will be hard to prove a foreign nation is responsible for acts of terrorism, said attorneys and professors with expertise in international law, who expected drawn-out legal wrangling.

"We may find that at the end of the day, after years of litigation, that the link is not sufficiently established even for Saudi Arabia," said Curtis Bradley, a law professor at Duke University.

The law says plaintiffs must show the foreign state "knowingly or recklessly provided material support or resources" to designated terrorist groups, not that the countries were simply negligent or looked the other way.

Congress on Wednesday overwhelming voted to pass the law, overturning President Barack Obama's veto. Before the law, American victims of terrorist acts could only sue countries designated by the U.S. State Department as state-sponsors of terrorism, currently Iran, Syria and Sudan.

Now, any country can be sued if there are allegations of support for known terrorists that carry out attacks on U.S. soil.

Existing tort law requires plaintiffs to prove that support played a "substantial factor" in the victims' injuries, a high bar, said Jimmy Gurule an expert in international criminal law at the University of Notre Dame.

This could be challenging in the Sept. 11 case since an independent commission on the 2001 attacks did not find sufficient evidence of Saudi involvement. Al-Qaeda claimed responsibility for the attacks and most of the 19 hijackers were Saudi nationals.

"We have a high degree of confidence we can meet that burden. The Saudis think we can't," said Jack Quinn, co-counsel for more than 2,000 family members of Sept. 11 victims.

The families sued Saudi Arabia in 2003, seeking to hold the country responsible. The proceedings have been stalled on the question of Saudi Arabia's immunity

Quinn said the plaintiffs will now ask the 2nd U.S. Circuit Court of Appeals to reconsider the issue in light of the new law.

If the court says the case can move forward, both sides will use discovery to seek documents and take depositions of witnesses and experts.

"We will next attempt to complete the development of evidence and find out what the truth is and on the basis of that, let the chips fall as they may," said Quinn.

LONG BATTLE AHEAD

But even under the new law, the White House can still request a court to halt this and other potential lawsuits.

The law allows a court to put a proceeding against a foreign state on hold if the United States says it "is engaged in good faith discussions" with the country to resolve the claims.

The stay provision and other changes were added to address concerns raised by the White House, Saudi Arabia and companies like General Electric and Dow Chemical Co.

Obama is likely to request such a stay, said Bradley.

Stephen Vladeck of the University of Texas School of Law, said this revision and others injected uncertainty into the law and could result in litigation aimed at clarifying the bill's language.

"The next step in this is either a whole bunch of lawsuits being placed on indefinite hold or a whole bunch of litigation to figure out the meaning of all these obstacles that Congress snuck back into the bill at the last minute," said Vladeck.

Even with the revisions, detractors of the new law worried that it could inspire other countries to retaliate by enacting their own statutes that could drag the United States or U.S. companies into court. Some U.S. lawmakers said Congress may revisit the law to narrow it further.

Ultimately, though, if the victims of terrorist acts win a court judgment against a foreign government, other cases have shown that collecting damages can be a slog.

A Reuters analysis last year found that in the 10 years following the Sept. 11 attacks, the number of lawsuits filed under the U.S. Anti-Terrorism Act and similar laws more than tripled compared to the decade before with plaintiffs winning billions of dollars worth of judgments in U.S. courts.

But judgments awarded against organizations or governments are often unenforceable and even when there are assets that can be claimed in the United States, their value often falls short of the award. (http://reut.rs/2dexDdV)

(Reporting by Mica Rosenberg; Editing by Noeleen Walder and David Gregorio)